The Annals of Statistics

Normalizing Transformatins and Bootstrap Confidence Intervals

Sadanori Konishi

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Abstract

This paper considers the problem of constructing approximate confidence intervals for functional parameters in the nonparametric case. The approach based on transformation theory is applied to improve standard confidence intervals. The accelerated bias-corrected percentile interval introduced by Efron relies on the existence of a normalizing transformation with bias and skewness corrections, although calculation does not require explicit knowledge of its functional form. We formally construct such a transformation and estimate bias and skewness correction factors for nonparametric situations. The resulting interval is shown to be second-order accurate. To this end Edgeworth expansions for the distributions of transformed statistics are derived, using the von Mises expansion.

Article information

Source
Ann. Statist., Volume 19, Number 4 (1991), 2209-2225.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176348393

Digital Object Identifier
doi:10.1214/aos/1176348393

Mathematical Reviews number (MathSciNet)
MR1135171

Zentralblatt MATH identifier
0745.62040

JSTOR
links.jstor.org

Subjects
Primary: 62E20: Asymptotic distribution theory
Secondary: 62G15: Tolerance and confidence regions

Keywords
Bootstrap confidence intervals Edgeworth expansions statistical functional transformations von Mises expansion

Citation

Konishi, Sadanori. Normalizing Transformatins and Bootstrap Confidence Intervals. Ann. Statist. 19 (1991), no. 4, 2209--2225. doi:10.1214/aos/1176348393. https://projecteuclid.org/euclid.aos/1176348393


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